A is 4x3 meaning that there are 4 rows and 3 columns.
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B is 3x4 meaning that there are 3 rows and 4 columns
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A matrix product is meaningful (exists) if and only if the number of columns of the first matrix equals the number of rows of the second matrix, i.e.
Apq X Bqr = Cpr

While Bqr X Apq does not exist unless r=q.

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